I have developed a new hatred for triangles

I have a triangle. It is a right triangle. The only side that has a known length is the hypotenuse. The other two angles are known. How do I determine the legth of the other two sides without knowing the sine, cosine, or tangent; OR if these are nescesary, how do I determine them with only the knowledge of the angles?

>>16
A = 30 degrees, S_1 = 1, S_2 = 1/2 allows only one triangle.

Or, more generally, if S_2 = sin(A)*S_1 then a unique triangle is determined.

(Note: S_1 is the side attached to the angle A, S_2 is the side opposite from the angle A)